Problem: Simplify the following expression: $ p = \dfrac{-3t - 8}{-2t - 5} - \dfrac{10}{3} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-3t - 8}{-2t - 5} \times \dfrac{3}{3} = \dfrac{-9t - 24}{-6t - 15} $ Multiply the second expression by $\dfrac{-2t - 5}{-2t - 5}$ $ \dfrac{10}{3} \times \dfrac{-2t - 5}{-2t - 5} = \dfrac{-20t - 50}{-6t - 15} $ Therefore $ p = \dfrac{-9t - 24}{-6t - 15} - \dfrac{-20t - 50}{-6t - 15} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-9t - 24 - (-20t - 50) }{-6t - 15} $ Distribute the negative sign: $p = \dfrac{-9t - 24 + 20t + 50}{-6t - 15}$ $p = \dfrac{11t + 26}{-6t - 15}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-11t - 26}{6t + 15}$